Presilting sequences for 0-Auslander extriangulated categories
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913148067381248 |
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| author | Nonis, Iacopo |
| author_facet | Nonis, Iacopo |
| contents | Let $\mathscr{C}$ be a reduced $0$-Auslander extriangulated category. Motivated by Pan--Zhu silting reduction for such categories, we introduce the notion of (signed) presilting sequences in $\mathscr{C}$ and establish a bijection between (signed) presilting sequences in $\mathscr{C}$ and (signed) $τ$-exceptional sequences over $Λ= \text{End}_{\mathscr{C}}(P)$, where $P$ is a projective generator of $\mathscr{C}$. This correspondence provides a new perspective on the Buan--Marsh bijection between signed $τ$-exceptional sequences and ordered support $τ$-rigid objects. Furthermore, we introduce a new category $\mathfrak{M}(\mathscr{C})$, called the $τ$-cluster morphism category of $\mathscr{C}$, whose objects are certain extension-closed subcategories of $\mathscr{C}$ and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the $τ$-cluster morphism category of $Λ$ from $\mathfrak{M}(\mathscr{C})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20957 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Presilting sequences for 0-Auslander extriangulated categories Nonis, Iacopo Representation Theory 16G10, 16G20, 16D90, 18G80 Let $\mathscr{C}$ be a reduced $0$-Auslander extriangulated category. Motivated by Pan--Zhu silting reduction for such categories, we introduce the notion of (signed) presilting sequences in $\mathscr{C}$ and establish a bijection between (signed) presilting sequences in $\mathscr{C}$ and (signed) $τ$-exceptional sequences over $Λ= \text{End}_{\mathscr{C}}(P)$, where $P$ is a projective generator of $\mathscr{C}$. This correspondence provides a new perspective on the Buan--Marsh bijection between signed $τ$-exceptional sequences and ordered support $τ$-rigid objects. Furthermore, we introduce a new category $\mathfrak{M}(\mathscr{C})$, called the $τ$-cluster morphism category of $\mathscr{C}$, whose objects are certain extension-closed subcategories of $\mathscr{C}$ and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the $τ$-cluster morphism category of $Λ$ from $\mathfrak{M}(\mathscr{C})$. |
| title | Presilting sequences for 0-Auslander extriangulated categories |
| topic | Representation Theory 16G10, 16G20, 16D90, 18G80 |
| url | https://arxiv.org/abs/2605.20957 |